1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 150,688 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 150,678 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      5
## 108  2020-06-16          East of England      2
## 109  2020-06-17          East of England      3
## 110  2020-03-01                   London      0
## 111  2020-03-02                   London      0
## 112  2020-03-03                   London      0
## 113  2020-03-04                   London      0
## 114  2020-03-05                   London      0
## 115  2020-03-06                   London      1
## 116  2020-03-07                   London      1
## 117  2020-03-08                   London      0
## 118  2020-03-09                   London      1
## 119  2020-03-10                   London      0
## 120  2020-03-11                   London      6
## 121  2020-03-12                   London      6
## 122  2020-03-13                   London     10
## 123  2020-03-14                   London     14
## 124  2020-03-15                   London     10
## 125  2020-03-16                   London     15
## 126  2020-03-17                   London     22
## 127  2020-03-18                   London     27
## 128  2020-03-19                   London     25
## 129  2020-03-20                   London     44
## 130  2020-03-21                   London     49
## 131  2020-03-22                   London     54
## 132  2020-03-23                   London     63
## 133  2020-03-24                   London     87
## 134  2020-03-25                   London    113
## 135  2020-03-26                   London    129
## 136  2020-03-27                   London    130
## 137  2020-03-28                   London    122
## 138  2020-03-29                   London    146
## 139  2020-03-30                   London    149
## 140  2020-03-31                   London    181
## 141  2020-04-01                   London    202
## 142  2020-04-02                   London    190
## 143  2020-04-03                   London    196
## 144  2020-04-04                   London    230
## 145  2020-04-05                   London    195
## 146  2020-04-06                   London    197
## 147  2020-04-07                   London    220
## 148  2020-04-08                   London    238
## 149  2020-04-09                   London    206
## 150  2020-04-10                   London    170
## 151  2020-04-11                   London    177
## 152  2020-04-12                   London    158
## 153  2020-04-13                   London    166
## 154  2020-04-14                   London    144
## 155  2020-04-15                   London    142
## 156  2020-04-16                   London    139
## 157  2020-04-17                   London    100
## 158  2020-04-18                   London    101
## 159  2020-04-19                   London    103
## 160  2020-04-20                   London     95
## 161  2020-04-21                   London     94
## 162  2020-04-22                   London    109
## 163  2020-04-23                   London     77
## 164  2020-04-24                   London     71
## 165  2020-04-25                   London     58
## 166  2020-04-26                   London     53
## 167  2020-04-27                   London     51
## 168  2020-04-28                   London     43
## 169  2020-04-29                   London     44
## 170  2020-04-30                   London     40
## 171  2020-05-01                   London     41
## 172  2020-05-02                   London     40
## 173  2020-05-03                   London     36
## 174  2020-05-04                   London     30
## 175  2020-05-05                   London     25
## 176  2020-05-06                   London     37
## 177  2020-05-07                   London     37
## 178  2020-05-08                   London     30
## 179  2020-05-09                   London     23
## 180  2020-05-10                   London     26
## 181  2020-05-11                   London     18
## 182  2020-05-12                   London     18
## 183  2020-05-13                   London     16
## 184  2020-05-14                   London     20
## 185  2020-05-15                   London     18
## 186  2020-05-16                   London     14
## 187  2020-05-17                   London     15
## 188  2020-05-18                   London      9
## 189  2020-05-19                   London     14
## 190  2020-05-20                   London     19
## 191  2020-05-21                   London     12
## 192  2020-05-22                   London     10
## 193  2020-05-23                   London      6
## 194  2020-05-24                   London      7
## 195  2020-05-25                   London      9
## 196  2020-05-26                   London     12
## 197  2020-05-27                   London      7
## 198  2020-05-28                   London      8
## 199  2020-05-29                   London      7
## 200  2020-05-30                   London     12
## 201  2020-05-31                   London      6
## 202  2020-06-01                   London     10
## 203  2020-06-02                   London      7
## 204  2020-06-03                   London      6
## 205  2020-06-04                   London      8
## 206  2020-06-05                   London      4
## 207  2020-06-06                   London      0
## 208  2020-06-07                   London      4
## 209  2020-06-08                   London      5
## 210  2020-06-09                   London      2
## 211  2020-06-10                   London      7
## 212  2020-06-11                   London      5
## 213  2020-06-12                   London      3
## 214  2020-06-13                   London      3
## 215  2020-06-14                   London      2
## 216  2020-06-15                   London      1
## 217  2020-06-16                   London      1
## 218  2020-06-17                   London      0
## 219  2020-03-01                 Midlands      0
## 220  2020-03-02                 Midlands      0
## 221  2020-03-03                 Midlands      1
## 222  2020-03-04                 Midlands      0
## 223  2020-03-05                 Midlands      0
## 224  2020-03-06                 Midlands      0
## 225  2020-03-07                 Midlands      0
## 226  2020-03-08                 Midlands      3
## 227  2020-03-09                 Midlands      1
## 228  2020-03-10                 Midlands      0
## 229  2020-03-11                 Midlands      2
## 230  2020-03-12                 Midlands      6
## 231  2020-03-13                 Midlands      5
## 232  2020-03-14                 Midlands      4
## 233  2020-03-15                 Midlands      5
## 234  2020-03-16                 Midlands     11
## 235  2020-03-17                 Midlands      8
## 236  2020-03-18                 Midlands     13
## 237  2020-03-19                 Midlands      8
## 238  2020-03-20                 Midlands     28
## 239  2020-03-21                 Midlands     13
## 240  2020-03-22                 Midlands     31
## 241  2020-03-23                 Midlands     33
## 242  2020-03-24                 Midlands     41
## 243  2020-03-25                 Midlands     48
## 244  2020-03-26                 Midlands     64
## 245  2020-03-27                 Midlands     72
## 246  2020-03-28                 Midlands     89
## 247  2020-03-29                 Midlands     92
## 248  2020-03-30                 Midlands     90
## 249  2020-03-31                 Midlands    123
## 250  2020-04-01                 Midlands    140
## 251  2020-04-02                 Midlands    142
## 252  2020-04-03                 Midlands    124
## 253  2020-04-04                 Midlands    151
## 254  2020-04-05                 Midlands    164
## 255  2020-04-06                 Midlands    140
## 256  2020-04-07                 Midlands    123
## 257  2020-04-08                 Midlands    186
## 258  2020-04-09                 Midlands    139
## 259  2020-04-10                 Midlands    127
## 260  2020-04-11                 Midlands    142
## 261  2020-04-12                 Midlands    139
## 262  2020-04-13                 Midlands    120
## 263  2020-04-14                 Midlands    116
## 264  2020-04-15                 Midlands    147
## 265  2020-04-16                 Midlands    102
## 266  2020-04-17                 Midlands    118
## 267  2020-04-18                 Midlands    115
## 268  2020-04-19                 Midlands     92
## 269  2020-04-20                 Midlands    107
## 270  2020-04-21                 Midlands     86
## 271  2020-04-22                 Midlands     78
## 272  2020-04-23                 Midlands    103
## 273  2020-04-24                 Midlands     79
## 274  2020-04-25                 Midlands     72
## 275  2020-04-26                 Midlands     81
## 276  2020-04-27                 Midlands     74
## 277  2020-04-28                 Midlands     68
## 278  2020-04-29                 Midlands     53
## 279  2020-04-30                 Midlands     56
## 280  2020-05-01                 Midlands     64
## 281  2020-05-02                 Midlands     51
## 282  2020-05-03                 Midlands     52
## 283  2020-05-04                 Midlands     61
## 284  2020-05-05                 Midlands     58
## 285  2020-05-06                 Midlands     59
## 286  2020-05-07                 Midlands     48
## 287  2020-05-08                 Midlands     34
## 288  2020-05-09                 Midlands     37
## 289  2020-05-10                 Midlands     42
## 290  2020-05-11                 Midlands     33
## 291  2020-05-12                 Midlands     45
## 292  2020-05-13                 Midlands     40
## 293  2020-05-14                 Midlands     37
## 294  2020-05-15                 Midlands     40
## 295  2020-05-16                 Midlands     34
## 296  2020-05-17                 Midlands     31
## 297  2020-05-18                 Midlands     34
## 298  2020-05-19                 Midlands     34
## 299  2020-05-20                 Midlands     36
## 300  2020-05-21                 Midlands     32
## 301  2020-05-22                 Midlands     27
## 302  2020-05-23                 Midlands     34
## 303  2020-05-24                 Midlands     19
## 304  2020-05-25                 Midlands     26
## 305  2020-05-26                 Midlands     33
## 306  2020-05-27                 Midlands     29
## 307  2020-05-28                 Midlands     27
## 308  2020-05-29                 Midlands     20
## 309  2020-05-30                 Midlands     20
## 310  2020-05-31                 Midlands     22
## 311  2020-06-01                 Midlands     20
## 312  2020-06-02                 Midlands     22
## 313  2020-06-03                 Midlands     24
## 314  2020-06-04                 Midlands     15
## 315  2020-06-05                 Midlands     21
## 316  2020-06-06                 Midlands     20
## 317  2020-06-07                 Midlands     16
## 318  2020-06-08                 Midlands     15
## 319  2020-06-09                 Midlands     17
## 320  2020-06-10                 Midlands     14
## 321  2020-06-11                 Midlands     13
## 322  2020-06-12                 Midlands     12
## 323  2020-06-13                 Midlands      6
## 324  2020-06-14                 Midlands     16
## 325  2020-06-15                 Midlands     11
## 326  2020-06-16                 Midlands      8
## 327  2020-06-17                 Midlands      1
## 328  2020-03-01 North East and Yorkshire      0
## 329  2020-03-02 North East and Yorkshire      0
## 330  2020-03-03 North East and Yorkshire      0
## 331  2020-03-04 North East and Yorkshire      0
## 332  2020-03-05 North East and Yorkshire      0
## 333  2020-03-06 North East and Yorkshire      0
## 334  2020-03-07 North East and Yorkshire      0
## 335  2020-03-08 North East and Yorkshire      0
## 336  2020-03-09 North East and Yorkshire      0
## 337  2020-03-10 North East and Yorkshire      0
## 338  2020-03-11 North East and Yorkshire      0
## 339  2020-03-12 North East and Yorkshire      0
## 340  2020-03-13 North East and Yorkshire      0
## 341  2020-03-14 North East and Yorkshire      0
## 342  2020-03-15 North East and Yorkshire      2
## 343  2020-03-16 North East and Yorkshire      3
## 344  2020-03-17 North East and Yorkshire      1
## 345  2020-03-18 North East and Yorkshire      2
## 346  2020-03-19 North East and Yorkshire      6
## 347  2020-03-20 North East and Yorkshire      5
## 348  2020-03-21 North East and Yorkshire      6
## 349  2020-03-22 North East and Yorkshire      7
## 350  2020-03-23 North East and Yorkshire      9
## 351  2020-03-24 North East and Yorkshire      8
## 352  2020-03-25 North East and Yorkshire     18
## 353  2020-03-26 North East and Yorkshire     21
## 354  2020-03-27 North East and Yorkshire     28
## 355  2020-03-28 North East and Yorkshire     35
## 356  2020-03-29 North East and Yorkshire     38
## 357  2020-03-30 North East and Yorkshire     64
## 358  2020-03-31 North East and Yorkshire     60
## 359  2020-04-01 North East and Yorkshire     67
## 360  2020-04-02 North East and Yorkshire     74
## 361  2020-04-03 North East and Yorkshire    100
## 362  2020-04-04 North East and Yorkshire    105
## 363  2020-04-05 North East and Yorkshire     92
## 364  2020-04-06 North East and Yorkshire     96
## 365  2020-04-07 North East and Yorkshire    102
## 366  2020-04-08 North East and Yorkshire    107
## 367  2020-04-09 North East and Yorkshire    111
## 368  2020-04-10 North East and Yorkshire    117
## 369  2020-04-11 North East and Yorkshire     98
## 370  2020-04-12 North East and Yorkshire     84
## 371  2020-04-13 North East and Yorkshire     94
## 372  2020-04-14 North East and Yorkshire    107
## 373  2020-04-15 North East and Yorkshire     96
## 374  2020-04-16 North East and Yorkshire    103
## 375  2020-04-17 North East and Yorkshire     88
## 376  2020-04-18 North East and Yorkshire     95
## 377  2020-04-19 North East and Yorkshire     88
## 378  2020-04-20 North East and Yorkshire    100
## 379  2020-04-21 North East and Yorkshire     76
## 380  2020-04-22 North East and Yorkshire     84
## 381  2020-04-23 North East and Yorkshire     63
## 382  2020-04-24 North East and Yorkshire     72
## 383  2020-04-25 North East and Yorkshire     69
## 384  2020-04-26 North East and Yorkshire     65
## 385  2020-04-27 North East and Yorkshire     65
## 386  2020-04-28 North East and Yorkshire     57
## 387  2020-04-29 North East and Yorkshire     69
## 388  2020-04-30 North East and Yorkshire     57
## 389  2020-05-01 North East and Yorkshire     64
## 390  2020-05-02 North East and Yorkshire     48
## 391  2020-05-03 North East and Yorkshire     40
## 392  2020-05-04 North East and Yorkshire     49
## 393  2020-05-05 North East and Yorkshire     40
## 394  2020-05-06 North East and Yorkshire     51
## 395  2020-05-07 North East and Yorkshire     45
## 396  2020-05-08 North East and Yorkshire     42
## 397  2020-05-09 North East and Yorkshire     44
## 398  2020-05-10 North East and Yorkshire     40
## 399  2020-05-11 North East and Yorkshire     29
## 400  2020-05-12 North East and Yorkshire     27
## 401  2020-05-13 North East and Yorkshire     28
## 402  2020-05-14 North East and Yorkshire     30
## 403  2020-05-15 North East and Yorkshire     32
## 404  2020-05-16 North East and Yorkshire     35
## 405  2020-05-17 North East and Yorkshire     26
## 406  2020-05-18 North East and Yorkshire     29
## 407  2020-05-19 North East and Yorkshire     27
## 408  2020-05-20 North East and Yorkshire     21
## 409  2020-05-21 North East and Yorkshire     33
## 410  2020-05-22 North East and Yorkshire     22
## 411  2020-05-23 North East and Yorkshire     18
## 412  2020-05-24 North East and Yorkshire     25
## 413  2020-05-25 North East and Yorkshire     21
## 414  2020-05-26 North East and Yorkshire     21
## 415  2020-05-27 North East and Yorkshire     22
## 416  2020-05-28 North East and Yorkshire     20
## 417  2020-05-29 North East and Yorkshire     25
## 418  2020-05-30 North East and Yorkshire     20
## 419  2020-05-31 North East and Yorkshire     20
## 420  2020-06-01 North East and Yorkshire     16
## 421  2020-06-02 North East and Yorkshire     22
## 422  2020-06-03 North East and Yorkshire     22
## 423  2020-06-04 North East and Yorkshire     17
## 424  2020-06-05 North East and Yorkshire     17
## 425  2020-06-06 North East and Yorkshire     21
## 426  2020-06-07 North East and Yorkshire     13
## 427  2020-06-08 North East and Yorkshire     11
## 428  2020-06-09 North East and Yorkshire     11
## 429  2020-06-10 North East and Yorkshire     16
## 430  2020-06-11 North East and Yorkshire      6
## 431  2020-06-12 North East and Yorkshire      8
## 432  2020-06-13 North East and Yorkshire     10
## 433  2020-06-14 North East and Yorkshire     11
## 434  2020-06-15 North East and Yorkshire      8
## 435  2020-06-16 North East and Yorkshire      9
## 436  2020-06-17 North East and Yorkshire      3
## 437  2020-03-01               North West      0
## 438  2020-03-02               North West      0
## 439  2020-03-03               North West      0
## 440  2020-03-04               North West      0
## 441  2020-03-05               North West      1
## 442  2020-03-06               North West      0
## 443  2020-03-07               North West      0
## 444  2020-03-08               North West      1
## 445  2020-03-09               North West      0
## 446  2020-03-10               North West      0
## 447  2020-03-11               North West      0
## 448  2020-03-12               North West      2
## 449  2020-03-13               North West      3
## 450  2020-03-14               North West      1
## 451  2020-03-15               North West      4
## 452  2020-03-16               North West      2
## 453  2020-03-17               North West      4
## 454  2020-03-18               North West      6
## 455  2020-03-19               North West      7
## 456  2020-03-20               North West     10
## 457  2020-03-21               North West     11
## 458  2020-03-22               North West     13
## 459  2020-03-23               North West     15
## 460  2020-03-24               North West     21
## 461  2020-03-25               North West     21
## 462  2020-03-26               North West     29
## 463  2020-03-27               North West     35
## 464  2020-03-28               North West     28
## 465  2020-03-29               North West     46
## 466  2020-03-30               North West     67
## 467  2020-03-31               North West     52
## 468  2020-04-01               North West     86
## 469  2020-04-02               North West     96
## 470  2020-04-03               North West     95
## 471  2020-04-04               North West     98
## 472  2020-04-05               North West    102
## 473  2020-04-06               North West    100
## 474  2020-04-07               North West    135
## 475  2020-04-08               North West    127
## 476  2020-04-09               North West    119
## 477  2020-04-10               North West    117
## 478  2020-04-11               North West    138
## 479  2020-04-12               North West    125
## 480  2020-04-13               North West    129
## 481  2020-04-14               North West    131
## 482  2020-04-15               North West    114
## 483  2020-04-16               North West    135
## 484  2020-04-17               North West     98
## 485  2020-04-18               North West    113
## 486  2020-04-19               North West     71
## 487  2020-04-20               North West     83
## 488  2020-04-21               North West     76
## 489  2020-04-22               North West     86
## 490  2020-04-23               North West     85
## 491  2020-04-24               North West     66
## 492  2020-04-25               North West     65
## 493  2020-04-26               North West     55
## 494  2020-04-27               North West     54
## 495  2020-04-28               North West     57
## 496  2020-04-29               North West     62
## 497  2020-04-30               North West     59
## 498  2020-05-01               North West     45
## 499  2020-05-02               North West     56
## 500  2020-05-03               North West     55
## 501  2020-05-04               North West     48
## 502  2020-05-05               North West     48
## 503  2020-05-06               North West     44
## 504  2020-05-07               North West     49
## 505  2020-05-08               North West     42
## 506  2020-05-09               North West     30
## 507  2020-05-10               North West     41
## 508  2020-05-11               North West     34
## 509  2020-05-12               North West     38
## 510  2020-05-13               North West     25
## 511  2020-05-14               North West     26
## 512  2020-05-15               North West     33
## 513  2020-05-16               North West     32
## 514  2020-05-17               North West     24
## 515  2020-05-18               North West     31
## 516  2020-05-19               North West     35
## 517  2020-05-20               North West     27
## 518  2020-05-21               North West     26
## 519  2020-05-22               North West     26
## 520  2020-05-23               North West     31
## 521  2020-05-24               North West     26
## 522  2020-05-25               North West     31
## 523  2020-05-26               North West     27
## 524  2020-05-27               North West     27
## 525  2020-05-28               North West     28
## 526  2020-05-29               North West     20
## 527  2020-05-30               North West     17
## 528  2020-05-31               North West     13
## 529  2020-06-01               North West     12
## 530  2020-06-02               North West     27
## 531  2020-06-03               North West     21
## 532  2020-06-04               North West     20
## 533  2020-06-05               North West     15
## 534  2020-06-06               North West     23
## 535  2020-06-07               North West     18
## 536  2020-06-08               North West     19
## 537  2020-06-09               North West     15
## 538  2020-06-10               North West     13
## 539  2020-06-11               North West     15
## 540  2020-06-12               North West      6
## 541  2020-06-13               North West      7
## 542  2020-06-14               North West     11
## 543  2020-06-15               North West     14
## 544  2020-06-16               North West      8
## 545  2020-06-17               North West      4
## 546  2020-03-01               South East      0
## 547  2020-03-02               South East      0
## 548  2020-03-03               South East      1
## 549  2020-03-04               South East      0
## 550  2020-03-05               South East      1
## 551  2020-03-06               South East      0
## 552  2020-03-07               South East      0
## 553  2020-03-08               South East      1
## 554  2020-03-09               South East      1
## 555  2020-03-10               South East      1
## 556  2020-03-11               South East      1
## 557  2020-03-12               South East      0
## 558  2020-03-13               South East      1
## 559  2020-03-14               South East      1
## 560  2020-03-15               South East      5
## 561  2020-03-16               South East      8
## 562  2020-03-17               South East      7
## 563  2020-03-18               South East     10
## 564  2020-03-19               South East      9
## 565  2020-03-20               South East     13
## 566  2020-03-21               South East      7
## 567  2020-03-22               South East     25
## 568  2020-03-23               South East     20
## 569  2020-03-24               South East     22
## 570  2020-03-25               South East     29
## 571  2020-03-26               South East     35
## 572  2020-03-27               South East     34
## 573  2020-03-28               South East     36
## 574  2020-03-29               South East     55
## 575  2020-03-30               South East     58
## 576  2020-03-31               South East     65
## 577  2020-04-01               South East     66
## 578  2020-04-02               South East     55
## 579  2020-04-03               South East     72
## 580  2020-04-04               South East     80
## 581  2020-04-05               South East     82
## 582  2020-04-06               South East     88
## 583  2020-04-07               South East    100
## 584  2020-04-08               South East     83
## 585  2020-04-09               South East    104
## 586  2020-04-10               South East     88
## 587  2020-04-11               South East     88
## 588  2020-04-12               South East     88
## 589  2020-04-13               South East     84
## 590  2020-04-14               South East     65
## 591  2020-04-15               South East     72
## 592  2020-04-16               South East     56
## 593  2020-04-17               South East     86
## 594  2020-04-18               South East     57
## 595  2020-04-19               South East     70
## 596  2020-04-20               South East     87
## 597  2020-04-21               South East     50
## 598  2020-04-22               South East     54
## 599  2020-04-23               South East     57
## 600  2020-04-24               South East     64
## 601  2020-04-25               South East     51
## 602  2020-04-26               South East     51
## 603  2020-04-27               South East     40
## 604  2020-04-28               South East     40
## 605  2020-04-29               South East     47
## 606  2020-04-30               South East     29
## 607  2020-05-01               South East     37
## 608  2020-05-02               South East     36
## 609  2020-05-03               South East     17
## 610  2020-05-04               South East     35
## 611  2020-05-05               South East     29
## 612  2020-05-06               South East     25
## 613  2020-05-07               South East     27
## 614  2020-05-08               South East     26
## 615  2020-05-09               South East     28
## 616  2020-05-10               South East     19
## 617  2020-05-11               South East     25
## 618  2020-05-12               South East     27
## 619  2020-05-13               South East     18
## 620  2020-05-14               South East     32
## 621  2020-05-15               South East     24
## 622  2020-05-16               South East     22
## 623  2020-05-17               South East     18
## 624  2020-05-18               South East     22
## 625  2020-05-19               South East     12
## 626  2020-05-20               South East     22
## 627  2020-05-21               South East     14
## 628  2020-05-22               South East     17
## 629  2020-05-23               South East     21
## 630  2020-05-24               South East     17
## 631  2020-05-25               South East     13
## 632  2020-05-26               South East     19
## 633  2020-05-27               South East     18
## 634  2020-05-28               South East     12
## 635  2020-05-29               South East     21
## 636  2020-05-30               South East      8
## 637  2020-05-31               South East     10
## 638  2020-06-01               South East     11
## 639  2020-06-02               South East     13
## 640  2020-06-03               South East     17
## 641  2020-06-04               South East     11
## 642  2020-06-05               South East     11
## 643  2020-06-06               South East     10
## 644  2020-06-07               South East     11
## 645  2020-06-08               South East      7
## 646  2020-06-09               South East      9
## 647  2020-06-10               South East     10
## 648  2020-06-11               South East      5
## 649  2020-06-12               South East      5
## 650  2020-06-13               South East      4
## 651  2020-06-14               South East      6
## 652  2020-06-15               South East      6
## 653  2020-06-16               South East      7
## 654  2020-06-17               South East      2
## 655  2020-03-01               South West      0
## 656  2020-03-02               South West      0
## 657  2020-03-03               South West      0
## 658  2020-03-04               South West      0
## 659  2020-03-05               South West      0
## 660  2020-03-06               South West      0
## 661  2020-03-07               South West      0
## 662  2020-03-08               South West      0
## 663  2020-03-09               South West      0
## 664  2020-03-10               South West      0
## 665  2020-03-11               South West      1
## 666  2020-03-12               South West      0
## 667  2020-03-13               South West      0
## 668  2020-03-14               South West      1
## 669  2020-03-15               South West      0
## 670  2020-03-16               South West      0
## 671  2020-03-17               South West      2
## 672  2020-03-18               South West      2
## 673  2020-03-19               South West      4
## 674  2020-03-20               South West      3
## 675  2020-03-21               South West      6
## 676  2020-03-22               South West      7
## 677  2020-03-23               South West      8
## 678  2020-03-24               South West      7
## 679  2020-03-25               South West      9
## 680  2020-03-26               South West     11
## 681  2020-03-27               South West     13
## 682  2020-03-28               South West     21
## 683  2020-03-29               South West     18
## 684  2020-03-30               South West     23
## 685  2020-03-31               South West     23
## 686  2020-04-01               South West     22
## 687  2020-04-02               South West     23
## 688  2020-04-03               South West     30
## 689  2020-04-04               South West     42
## 690  2020-04-05               South West     32
## 691  2020-04-06               South West     34
## 692  2020-04-07               South West     39
## 693  2020-04-08               South West     47
## 694  2020-04-09               South West     24
## 695  2020-04-10               South West     46
## 696  2020-04-11               South West     43
## 697  2020-04-12               South West     23
## 698  2020-04-13               South West     27
## 699  2020-04-14               South West     24
## 700  2020-04-15               South West     32
## 701  2020-04-16               South West     29
## 702  2020-04-17               South West     33
## 703  2020-04-18               South West     25
## 704  2020-04-19               South West     31
## 705  2020-04-20               South West     26
## 706  2020-04-21               South West     26
## 707  2020-04-22               South West     23
## 708  2020-04-23               South West     17
## 709  2020-04-24               South West     19
## 710  2020-04-25               South West     15
## 711  2020-04-26               South West     27
## 712  2020-04-27               South West     13
## 713  2020-04-28               South West     17
## 714  2020-04-29               South West     15
## 715  2020-04-30               South West     26
## 716  2020-05-01               South West      6
## 717  2020-05-02               South West      7
## 718  2020-05-03               South West     10
## 719  2020-05-04               South West     17
## 720  2020-05-05               South West     14
## 721  2020-05-06               South West     19
## 722  2020-05-07               South West     16
## 723  2020-05-08               South West      6
## 724  2020-05-09               South West     11
## 725  2020-05-10               South West      5
## 726  2020-05-11               South West      8
## 727  2020-05-12               South West      7
## 728  2020-05-13               South West      7
## 729  2020-05-14               South West      6
## 730  2020-05-15               South West      4
## 731  2020-05-16               South West      4
## 732  2020-05-17               South West      6
## 733  2020-05-18               South West      4
## 734  2020-05-19               South West      6
## 735  2020-05-20               South West      1
## 736  2020-05-21               South West      9
## 737  2020-05-22               South West      6
## 738  2020-05-23               South West      6
## 739  2020-05-24               South West      3
## 740  2020-05-25               South West      8
## 741  2020-05-26               South West     11
## 742  2020-05-27               South West      5
## 743  2020-05-28               South West     10
## 744  2020-05-29               South West      7
## 745  2020-05-30               South West      3
## 746  2020-05-31               South West      2
## 747  2020-06-01               South West      7
## 748  2020-06-02               South West      2
## 749  2020-06-03               South West      5
## 750  2020-06-04               South West      2
## 751  2020-06-05               South West      2
## 752  2020-06-06               South West      1
## 753  2020-06-07               South West      3
## 754  2020-06-08               South West      3
## 755  2020-06-09               South West      0
## 756  2020-06-10               South West      0
## 757  2020-06-11               South West      2
## 758  2020-06-12               South West      2
## 759  2020-06-13               South West      2
## 760  2020-06-14               South West      0
## 761  2020-06-15               South West      0
## 762  2020-06-16               South West      0
## 763  2020-06-17               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-18"

The completion date of the NHS Pathways data is Thursday 18 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -9.215  -2.760  -0.260   2.834   4.805  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.965e+00  5.240e-02   94.75   <2e-16 ***
## note_lag    1.147e-05  5.217e-07   21.99   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 10.59199)
## 
##     Null deviance: 5488.03  on 47  degrees of freedom
## Residual deviance:  501.66  on 46  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  143.356267    1.000011
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 129.21939 158.690218
## note_lag      1.00001   1.000012

Rsq(lag_mod)
## [1] 0.9085905

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.1       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0